Question: Solve for $x$ and $y$ using substitution. ${-4x+3y = -1}$ ${y = -5x+6}$
Since $y$ has already been solved for, substitute $-5x+6$ for $y$ in the first equation. ${-4x + 3}{(-5x+6)}{= -1}$ Simplify and solve for $x$ $-4x-15x + 18 = -1$ $-19x+18 = -1$ $-19x+18{-18} = -1{-18}$ $-19x = -19$ $\dfrac{-19x}{{-19}} = \dfrac{-19}{{-19}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {y = -5x+6}\thinspace$ to find $y$ ${y = -5}{(1)}{ + 6}$ $y = -5 + 6$ $y = 1$ You can also plug ${x = 1}$ into $\thinspace {-4x+3y = -1}\thinspace$ and get the same answer for $y$ : ${-4}{(1)}{ + 3y = -1}$ ${y = 1}$